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On the relation between the mean and variance of delay in dynamic queues with random capacity and demand

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  • Fosgerau, Mogens

Abstract

This paper investigates the distribution of delays during a repeatedly occurring demand peak in a congested facility with random capacity and demand, such as an airport or an urban road. Congestion is described in the form of a dynamic queue using the Vickrey bottleneck model and assuming Nash equilibrium in arrival times. The paper shows that the expected delay and the variance of delay vary differently over time during the peak and must hence be considered separately. The paper gives some characterization of how the expected delay and the variance of delay are related, which explain the looping phenomenon that has now been observed a number of times. Empirical illustration is provided.

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File URL: http://mpra.ub.uni-muenchen.de/11994/
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File URL: http://mpra.ub.uni-muenchen.de/42266/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 11994.

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Date of creation: 2008
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Handle: RePEc:pra:mprapa:11994

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Related research

Keywords: Bottleneck model; Random capacity; Congestion; Nash Equilibrium; Loop;

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References

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  1. Fosgerau, Mogens & Engelson, Leonid, 2011. "The value of travel time variance," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 1-8, January.
  2. Richard Arnott & Andre de Palma & Robin Lindsey, 1996. "Information and Time-of-Usage Decisions in the Bottleneck Model with Stochastic Capacity and Demand," Boston College Working Papers in Economics 355., Boston College Department of Economics.
  3. Fosgerau, Mogens & Karlström, Anders, 2007. "The value of reliability," MPRA Paper 5733, University Library of Munich, Germany.
  4. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1993. "A Structural Model of Peak-Period Congestion: A Traffic Bottleneck with Elastic Demand," American Economic Review, American Economic Association, vol. 83(1), pages 161-79, March.
  5. Fosgerau, Mogens, 2008. "Congestion costs in bottleneck equilibrium with stochastic capacity and demand," MPRA Paper 10040, University Library of Munich, Germany.
  6. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May.
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Citations

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Cited by:
  1. Fosgerau, Mogens & Lindsey, Robin, 2013. "Trip-timing decisions with traffic incidents," MPRA Paper 48708, University Library of Munich, Germany.
  2. Koster, Paul & Kroes, Eric & Verhoef, Erik, 2011. "Travel time variability and airport accessibility," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1545-1559.
  3. repec:dgr:uvatin:2011181 is not listed on IDEAS
  4. Fosgerau, Mogens & Fukuda, Daisuke, 2010. "Valuing travel time variability: Characteristics of the travel time distribution on an urban road," MPRA Paper 24330, University Library of Munich, Germany.
  5. André De Palma & Mogens Fosgerau, 2010. "Dynamic and Static congestion models: A review," Working Papers hal-00539166, HAL.

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